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How do you graph the inequality #-2x+y>=-4#?

Answer 1

Step 1. Dashed or Solid Line

This inequality says that #-2x+y# is greater than or equal to #-4#. That means that our graph will be a solid line (as opposed to a dashed line).

Step 2. Graph it, pretending it's an equation (not an inequality).

This is easier to solve if you pretend you have a linear equation instead of an inequality. That is, determine what you would graph if you were asked

#-2x+y=-4#

#y=2x-4#

But sure to graph it with a solid line (see Step 1).

graph{2x-4[-2,5,-5,5]}

Step 3. Pick points to decide which side to shade.

Going back to the original inequality, #-2x+y>=-4#, you should plug in points to see where the inequality is TRUE or FALSE. A good point to pick is always the origin, #(0,0)#.

#-2x+y>=-4#

#-2(0)+0>=-4#

#0>=-4# is TRUE, so shade on the side of the line containing the point #(0,0)#. The graph looks like this.

graph{(y-2x+4)>=0[-2,5,-5,5]}

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Answer 2

Julia Adams

To graph the inequality -2x + y ≥ -4, follow these steps:

First, graph the boundary line y = 2x - 4.
Since the inequality is "greater than or equal to," shade the area above the boundary line.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you graph the inequality #-2x+y&gt;=-4#?

How do you graph the inequality #-2x+y>=-4#?